David Aristoff's homepage Title: Active Subspaces: Emerging Ideas for Dimension Reduction in Highly Parameterized Computational Science Models

Abstract: Scientists and engineers use computer simulations to study relationships between a physical model's input parameters and its output predictions. However, thorough parameter studies---e.g., constructing response surfaces, optimizing, or averaging---are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are part of an emerging set of subspace-based dimension reduction tools that identify important directions in the input parameter space with respect to a particular model output. I will describe methods for discovering a model's active subspaces and propose strategies for exploiting the reduced dimension to enable otherwise infeasible parameter studies. For more information, see activesubspaces.org